man.diff

来自「speech signal process tools」· DIFF 代码 · 共 352 行

.\" @(#)wmse_filt.1e	3.9	5/24/91 ESI
.TH WMSE_FILT 1\-ESPS 5/24/91
.ds ]W "\fI\s+4\ze\h'0.05'e\s-4\v'-0.4m'\fP\(*p\v'0.4m'\ Entropic Processing, Inc.
.SH NAME
wmse_filt \- design an FIR filter using the weighted mean square error criterion.
.sp
.SH SYNOPSIS
.B wmse_filt
[
.BI \-x " debug_level"
]
[
.BI \-c " comment"
]
[
.BI \-n " nsiz"
]
[
.BI \-d " d_file"
]
[
.BI \-w " w_file"
]
.I feafilt_file
.sp
.SH DESCRIPTION
.PP
The program
.I wmse_filt
designs a linear phase finite impulse response (FIR) 
filter and prints the coefficients to the FEAFILT file
.I feafilt_file.
The user specifies the number of coefficients, the desired
filter frequency response, and a weighting function.  The program then finds the
set of filter coefficients that minimizes the mean square error between
the desired response and the actual response, when weighted by the weighting
function.  In other words, for desired response 
.I D(f), 
and weighting function 
.I W(f),
the program finds the filter 
.I H(f)
which minimizes:
.nf
.ce
.if t \{
.EQ
.nr 99 \n(.s
.nr 98 \n(.f
.ps 10
.ft 2
.ds 11 \s10\v'.1m'\s+4\(is\s-4\v'-.1m'\s10
.ds 12 "\(miFS\|\(sl\f12\fP
.ds 13 "FS\|\(sl\f12\fP
.nr 11 \w'\s10\*(11'
.nr 14 \n(11
.nr 12 \w'\s7\*(12'
.if \n(12>\n(14 .nr 14 \n(12
.nr 13 \w'\s7\*(13'
.if \n(13>\n(14 .nr 14 \n(13
.ds 14 \v'60u'\h'\n(14u-\n(12u/2u'\s7\*(12\s10\h'-\n(14u-\n(12u/2u'\v'-60u'\
\h'\n(14u-\n(11u/2u'\*(11\h'\n(14u-\n(11u/2u'\
\v'-78u'\h'-\n(14u-\n(13u/2u'\s7\*(13\s10\h'\n(14u-\n(13u/2u'\v'78u'\

.ds 11 "\|
.as 14 "\*(11
.ds 11 "\|
.ds 12 "D\|\f1(\fP\^f\|\|\f1)\fP
.as 11 "\*(12
.ds 12 "\(mi
.as 11 "\*(12
.ds 12 "H\|\f1(\fP\^f\|\|\f1)\fP
.as 11 "\*(12
.ds 11 \|\v'-6u'\b'\(bv\(bv'\v'6u'\*(11\|\v'-6u'\b'\(bv\(bv'\v'6u'
.ds 12 "\f12\fP
.as 11 \v'-24u'\s-3\*(12\s+3\v'24u'
.ds 12 "\ 
.as 11 "\*(12
.ds 12 "W\|\f1(\fP\^f\|\|\f1)\fP
.as 11 "\*(12
.as 14 "\*(11
.ds 11 "\ 
.as 14 "\*(11
.ds 11 "d\^f\|
.as 14 "\*(11
.ds 14 \x'0'\x'0-48u'\f2\s10\*(14\|\s\n(99\f\n(98\x'48u'
.nr 14 \w'\*(14'
.nr MK 0
.if 180>\n(.v .ne 180u
.rn 14 10
\*(10
.ps \n(99
.ft \n(98
.EN
\}
.if n \{
integral (from -FS/2 to FS/2) of |D(f)-H(f)|(squared) * W(f) df
\}
.fi
.PP
The user may specify the desired frequency response and the 
weighting function in one of two
modes: \fIprompt\fR and \fIpointwise\fR.
.PP
In "prompt mode" the program assumes that the desired frequency response and
the weighting function are constant throughout a number of frequency bands.
The user is then prompted for the sampling frequency in Hertz (\fIFS\fR), 
the number of 
frequency bands in the range
from zero to half the sampling frequency, the edge of each band in Hertz, 
the relative
gain in each band, and the weighting value of each band. 
All lists of numbers are separated by white space.
See the \fIFiltering Sampled Data\fP Applications note for several
design examples.
.PP
The relative gain
values specify the magnitude response of the filter. 
Thus, a bandpass gain
specification of { .5  1  .5 } results in a pass band with 0 dB gain
and two stop bands with 6 dB of loss. Specifying 0 gain in a band
results in the maximum possible loss in that band that is consistent
with the rest of the filter specification.
(A negative number for the band gain may be specified
in order to achieve negative (sign reversing) gain, 
but the relative magnitudes of
the bands are maintained independent of the sign of the gains.)
The weighting function allows the user to reduce the approximation
error in designated high-weight bands relative to the lesser weighted bands.
If the desired filter design-approximation-error is to be spread uniformly
across all the bands, then identical, non-zero weights
should be specified.
The weighting function values, however, must not be negative.
The user is prompted for all the design information
on the standard output.  
The first band always starts at zero Hz. and the last band always ends at
half the sampling frequency (\fIFS\fP/2).
Since the bands are assumed contiguous, the user will only enter 
.I "nbands+1"
edges for
.I nbands
bands.
.PP
In "pointwise mode" the program allows the desired frequency response 
and the weighting function to be arbitrarily shaped and specified at
a number of uniformly spaced points from zero to half the sampling frequency.
The number of points must be one plus a power of two.  The point values of
the desired response and the weighting function
are specified in the ascii files 
.I d_file
and
.I w_file
respectively.  
The first number in each of these files
should be an integer which tells how many point values are
in the file.  The point values follow.
Data in both files may be separated by any combination
of spaces or newlines.  The desired response and the weighting function may
be in the same file, in which case the desired response comes
first and the same file must be specified as both the
.I d_file
and the
.I w_file
above.
.PP
The prompt mode is more accurate than the point mode if the desired 
frequency response
and the weighting function are of the constant region form 
described above.
.PP
The program prompts the user for comments to be added to the comment field of
.I feafilt_file
unless the 
.B \-c 
option is used.
The user should type in his comments and terminate
them with a ^D on a line by itself.  
The user added comment is limited to 2047
characters.
.PP
If
.I feafilt_file
is "\-", the output is to the standard output.
.sp
.SH OPTIONS
The following options are supported:
.TP
.BI \-x " debug_level"
A value of 0 (the default value) will cause
.I wmse_filt
to do its work silently, unless there is an error.
A nonzero value will cause various parameters to be printed out
during program initialization.
.br
.TP
.BI \-c " comment"
The character string
.I comment
is added to the comment field of the output file header.  If this option is not used,
the program prompts the user for a comment string.
When prompted by the program,
the user should terminate the comment string  with
a ^D.
.br
.TP
.BI \-n " nsiz"
The number of coefficients in the filter.  If this option is not used 
.I wmse_filt
will prompt for the number regardless of whether the user is in prompt
mode or pointwise mode.
The number of coefficients must be odd.
.br
.TP
.BI \-d " d_file"
The ascii file specifying the pointwise desired filter magnitude response.  The first
number in this file should be an integer, telling how many points
are in the file, which should be a power of two plus one.  Using this option
will place the user in pointwise mode, and the user must also specify a 
weighting function file using the
.B \-w 
option or he will be prompted for it.  
Points on the desired response may be negative in order to achieve
negative gain.  For best results, 
.I d_file
should contain a minimum of 513 or
.I nsiz
(whichever is larger) points.
.br
.TP
.BI \-w " w_file"
The ascii file containing the pointwise weighting function.  If the user is in 
the pointwise mode and does not specify 
.I w_file
he will be prompted for it.  If he specifies "\-" for 
.I w_file,
uniform weighting (i.e. everywhere equal to 1.0) will be used.
Weighting function point values may not be negative.
The first number in this file should be an integer telling how many
point values are in the file, which should be equal to the number of
desired response point values.
For best results, this file should contain
a minimum of 513 or
.I nsiz
(whichever is larger) points.
.sp
.SH ESPS PARAMETERS
The parameter file is not read.
.sp
.SH ESPS COMMON
The common file is neither read nor written.
.SH ESPS HEADER
A new FEAFILT header is created for the output file.
The program fills in appropriate values in the common part of the header
as well as the following generic header items associated with the FEAFILT 
file type.
.sp
.IP
.I max_num
.IP
Set to
.I nsiz.
.sp
.IP
.I max_denom
.IP
This value is always set to 0.
.sp
.IP
.I define_pz, complex_filter
.IP
These values are set to NO.
.sp
.IP
.I func_spec
.IP
This value is set to BAND when in the prompt mode and POINT when in
the pointwise mode.
.sp
.IP
.I nbands
.IP
This value is filled in appropriately when the prompt mode is used.
.sp
.IP
.I npoints
.IP
This value is filled in appropriately when the pointwise mode is used.
.sp
.IP
.I type
.IP
This value is set to FILT_ARB.
.sp
.IP
.I method
.IP
This value is always set to WMSE.
.sp
.IP
.I bandedges
.IP
This array is filled in appropriately for the prompt mode.
.sp
.IP
.I points
.IP
This array is filled in appropriately for the pointwise mode.
.sp
.IP
.I gains
.IP
This array is filled in with the band gains when in the prompt mode
and with the point gains when in the pointwise mode.
.sp
.IP
.I wts
.IP
This array is filled in with the band weights when in the prompt mode
and with the point weights when in the pointwise mode.
.PP
In addition, the generic header items \fIsamp_freq\fR (type DOUBLE)
and \fIdelay_samples\fP (type DOUBLE)
are added to the header. \fIDelay_samples\fP is equal to (\fInsiz\fP \- 1)/2.
This represents the delay to the center of the peak of the impulse response.
.sp
.SH DIAGNOSTICS
The program will print an error message to standard error if the above specifications
are not met.
The error messages are intended to 
be self explanatory.
.sp
.SH FILES
When
.I debug_level
is nonzero, the program prints arrays to the files "harray", "warray", and
"hwarray" in the format used by printarr (3-ESPS).  These arrays are the time
domain values of the desired response, the weighting function, and the
convolution of these two responses, respectively.
.sp
.SH SEE ALSO
FEAFILT (5-ESPS), feafilter (1-ESPS), fft_filter (1-ESPS), impulse_resp (1-ESPS),
notch_filter (1-ESPS), zero_pole (1-ESPS), atofilt (1-ESPS), iir_filt (1-ESPS),
xpz (1-ESPS), zero_pole (1-ESPS)
.sp
.SH BUGS
The program currently only designs filters with an odd 
number of coefficients.
.sp
.SH AUTHOR
Brian Sublett; modified for ESPS 3.0 by David Burton